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A Semiclassical Approach to the Dirac Equation

✍ Scribed by Jens Bolte; Stefan Keppeler

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
273 KB
Volume
274
Category
Article
ISSN
0003-4916

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✦ Synopsis

We derive a semiclassical time evolution kernel and a trace formula for the Dirac equation. The classical trajectories that enter the expressions are determined by the dynamics of relativistic point particles. We carefully investigate the transport of the spin degrees of freedom along the trajectories which can be understood geometrically as parallel transport in a vector bundle with SU(2) holonomy. Furthermore, we give an interpretation in terms of a classical spin vector that is transported along the trajectories and whose dynamics, dictated by the equation of Thomas precession, gives rise to dynamical and geometric phases every orbit is weighted by. We also present an analogous approach to the Pauli equation which we analyse in two different limits.

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